If α and β are the roots of $x^2-5x+2=0$, then α⁴ + β⁴ equals:

Here α + β = 5 and αβ = 2, so α² + β² = 25 − 4 = 21. Squaring that pair in turn, α⁴ + β⁴ = $({\alpha }^2+{\beta }^2{)}^2-2(\alpha \beta {)}^2=441-2(4)=433$. (441 stops at the square and forgets the correction term; 437 subtracts 2αβ = 4 instead of 2$(\alpha \beta {)}^2=8$; 617 uses $(\alpha +\beta {)}^4=625$ in place of $({\alpha }^2+{\beta }^2{)}^2$.) The roots are (5 ± √17)/2 ≈ 4.5616 and 0.4384, whose fourth powers ≈ 432.96 and 0.037 add to 433.